The Spain international was ruled out of the 3-2 victory over Tottenham late on with a calf injury and has been receiving treatment since.
But Mike Marsh, the first-team coach at Anfield, is confident Reina's fitness will improve enough for the goalkeeper to be involved again against Saints at St Mary's.
|7/2||Southampton are 7/2 with Coral to beat Liverpool
"He's coming along nicely," Marsh told the club's official website. "He's got one of those injuries where you're not sure how long it's going to take.
"He's still getting treatment - with a bit of luck that will improve in the next couple of days and he'll be available for Saturday."
Marsh also indicated the scheduling of Joe Allen's shoulder surgery depends on the fitness of the rest of the Liverpool squad.
He continued: "I think he will need surgery. We'll try to get that out of the way sooner rather than later so he'll be ready for pre-season.
"We'll just see how the rest of the squad is before we commit to that."